Will Percival The University of Portsmouth The Theory/Observation connection lecture 4 dark energy: linking with observations Will Percival The University of Portsmouth

Lecture outline Dark Energy review Geometrical tests cosmological constant? quintessence? tangled defects? phantom dark energy? modified gravity? problems with the data? Geometrical tests SN1a BAO

Cosmological constant Originally introduced by Einstein to make the Universe static Constant vacuum energy density, which is homogeneous and has constant density in time Equation of state Particle physics provides a natural candidate: zero-point vacuum fluctuations for bosonic or fermionic fields typical scale of cosmological constant is (Mcutoff)4, where Mcutoff is UV cutoff of theory describing field Planck mass gives planck ~ (1019GeV)4 Observations show

quintessence adaption of scalar field theory developed for inflationary theories for late-time dark energy very weak potential required, with very small effective mass field can be frozen at early times or it can slowly roll down the potential, with energy density tracking dominant fluid until recently (“tracker” models) equation-of-state generally evolves, although can be constant (with special choice of potential) In fact, any w(z)>-1 history can be obtained with right choice of potential

Albrecht & Weller 2002, astro-ph/0106079 quintessence Albrecht & Weller 2002, astro-ph/0106079

Parameterizations of w If you don’t know the physics, you don’t have a well-defined set of models to test, it’s a free-for-all can parameterise using w(a) = w0 + w1(1-a) Bassett et al. 2004, astro-ph/0407364

Tangled defects Network of defects formed in phase transition grows with expansion of Universe For strings, lengths grow as a, and energy as a-2, so w=-1/3, and no acceleration (just) For walls, area grows as a2, and energy drops as a-1, so w=-2/3, which can produce acceleration but observations show w ~ -1

Phantom dark energy motivated by early supernovae data which favored strong acceleration w<-1 density increases as Universe expands can lead to divergence in finite time - big rip theoretically difficult to justify violate weak energy condition lead to ghosts - negative norm energy states can be classically and quantum mechanically unstable If observations continue to show strong acceleration at low redshifts, may need a phase shift in theory

modified gravity Can separate cosmological constant from stress-energy tensor Can then imagine moving it to the other side of the equation Should we consider alternatives if we’re going to be modifying gravity, rather than postulating a new component of energy?

modified gravity Example from history: Mercury perihilion Newton + dark planet? No! Modified gravity (GR) Today, we need a modified Friedmann equation

modified gravity Modified gravity: replace R with f(R) in action for gravity. Gives DGP modifed gravity (5D braneworld) Problem: we can always explain Adark by either stress-energy component or change to gravity. Only way of telling apart is by structure formation (see next lecture)

Problems with the data … data depends on astrophysics, so subject to systematics but, more than one test, so need a conspiracy that all the astrophysics points you to acceleration … Still, worth reviewing all data

With this in mind, lets have a look at the evidence for acceleration …

All strong evidence is geometrical All of the evidence depends on the expansion geometry, specifically through the Friedmann equation equation of state of dark energy p = w(a) 

<w>=-1.02 ± 0.09 (stat) ± 0.054 (sys) (with BAO + Flat Universe) SNLS Hubble diagram First-Year SNLS Hubble Diagram Astier et al (2006) A&A, 447, 31 ΩM = 0.263 ± 0.042 (stat) ± 0.032 (sys) <w>=-1.02 ± 0.09 (stat) ± 0.054 (sys) (with BAO + Flat Universe)

Supernovae observations Initially assumed all SN1a have same intrinsic peak brightness Now refined so that Apparent magnitude of supernova Stretch parameter s: corrects for lightcurve shape via  Luminosity distance to supernova Absolute magnitude of supernova (assumed constant for all SN1a) c=B-V colour: corrects for extinction/intrinsic effects via 

Supernovae systematics “Experimental Systematics” Calibration, photometry, Malmquist-type effects Contamination by other SNe or peculiar SNe Ia Minimized by spectroscopic confirmation Non-SNe systematics Peculiar velocities; Hubble Bubble; Weak lensing K-corrections and SN spectra UV uncertain; “golden” redshifts; spectral evolution? Extinction/Colour Effective RV; Intrinsic colour versus dust Redshift evolution in the mix of SNe “Population drift” – environment? Evolution in SN properties Light-curves/Colors/Luminosities From talk by Mark Sullivan

Hubble diagram by galaxy type SNe in passive galaxies show a smaller scatter “Intrinsic dispersion” consistent with zero (Does intrinsic dispersion in SNe arise from dust?) Cleaner sample: But SNe in passive galaxies are at high-z (~20%: two component model) + very few locally Star-forming hosts Passive hosts

Cosmological distribution of galaxy types

Future supernovae prospects Short-term: Current constraints on <w>: <w>=-1 to ~6-7% (stat) (inc. flat Universe, BAO+WMAP-3) At SNLS survey end, statistical uncertainty will be 4-5%: 500 SNLS + 200 SDSS + larger local samples Improved external constraints (BAO, WL) Longer term: No evolutionary bias in cosmology detected (tests continue!) SNe in passive galaxies: seem more powerful probes, but substantially rarer (esp. at high-z) Colour corrections are the dominant uncertainty Urgent need for z<0.1 samples with wide wavelength coverage Not clear what the “next step” at high-z should be

Galaxy clustering

The power spectrum turn-over In radiation dominated Universe, pressure support means that small perturbations cannot collapse. Jeans scale changes with time, leading to smooth turn-over of matter power spectrum. varying the matter density times the Hubble constant However, it is hard to disentangle this shape change from galaxy bias and non-linear effects

Problem: galaxy bias Galaxies do not form a Poisson sampling of the matter field Peaks model: large scale offset in 2-pt clustering strength (next lecture) Also non-linear effects in the matter Also effects from the transition from mass to galaxies Angulo et al., 2007, MNRAS, astro-ph/0702543

Baryon Acoustic Oscillations “Wavelength” of baryonic acoustic oscillations is determined by the comoving sound horizon at recombination varying the baryon fraction At early times can ignore dark energy, so comoving sound horizon is given by Sound speed cs Gives the comoving sound horizon ~110h-1Mpc, and BAO wavelength 0.06hMpc-1

CREDIT: WMAP & SDSS websites Comparing CMB & BAO CMB SDSS GALAXIES CREDIT: WMAP & SDSS websites

Comparing BAO at different redshifts SDSS main galaxies + 2dFGRS SDSS LRGs Tell us more about the acceleration, rather than just that we need it! z=0.2 z=0.35 CREDIT: WMAP & SDSS websites

BAO as a standard ruler Gives rise to the “rings of power” Changes in cosmological model alter measured BAO scale (∆dcomov) by: Radial direction (evolution of Universe) Angular direction (line of sight) Gives rise to the “rings of power” Hu & Haiman 2003, astro-ph/0306053

BAO as a standard ruler BAO position (in a redshift slice) therefore constrains some multiple of Changes in cosmological model alter measured BAO scale (∆dcomov) by: Radial direction (evolution of Universe) Angular direction (line of sight) If we are considering radial and angular directions using randomly placed galaxy pairs, we constrain (to 1st order) Varying rs/DV

Why BAO are a good ruler Linear baryon acoustic oscillations are ratio of linear matter power spectrum to a smooth fit Suppose that we measure an observed power that is related to the linear power by (halo model) Linear bias model also predicts this form Then observed oscillations are related to linear BAO by For linear bias model, peculiar velocities of galaxies gives Gaussian damping with width ~10Mpc No change in position of oscillations, just a damping term. To change the observed positions of BAO, we need sharp features in the observed power Eisenstein, Seo & White 2006, astro-ph/0604361 Percival et al. 2007, astro-ph/0705.3323

“Renormalized Perturbation Theory (RPT)” Going to 2nd order … Perturbative treatment of (CDM+baryon) fluid system （e.g., Suto & Sasaki 1991) New approach Based on field-theoretical approach, Standard PT calculation can be improved by re-summing an infinite class of perturbative corrections at all orders. “Renormalized Perturbation Theory (RPT)” Crocce & Scoccimarro (2006ab,2007) Related works: McDonald, Matarrese & Pietroni, Valageas, Matsubara (‘07)

Going to 2nd order … At second order we get mode mixing, which causes shifts in the power spectrum BAO peaks Shifts are <1%, and can be calculated Not important for current data, but need to be included for future analyses Crocce & Scoccimarro 2007; astro-ph/0704.2783

BAO from all the SDSS DR5 galaxies Compared with WMAP 3-year best fit linear CDM cosmological model. N.B. not a fit to the data, but a prediction from WMAP. Interesting features: Overall P(k) shape Observed baryon acoustic oscillations (BAO) Percival et al., 2007, ApJ, 657, 645

BAO from the 2dFGRS + SDSS BAO detected at low redshift 0<z<0.3 (effective redshift 0.2) BAO detected at high redshift 0.15<z<0.5 (effective redshift 0.35) BAO from combined sample (detected over the whole redshift range 0<z<0.5) Percival et al., 2007, MNRAS, astro-ph/0705.3323

BAO distance scale constraints Constraint including observed peak distance constrain from CMB rs/dA(cmb)=0.0104 CDM OCDM SCDM Constraint fitting rs/DV(z) Constraint from DV(0.35)/DV(0.2)

Future BAO prospects Short-term: SDSS-II improves low redshift measurements by factor ~2 1000000 galaxy redshifts to z~0.5 Wiggle-Z survey detects BAO at higher redshift 400 000 galaxy redshifts to z~1 weak constraints Longer term: Photometric surveys (e.g PanSTARRS, DES) find ~2--3% distance constraints out to z~1 Future spectroscopic surveys (e.g. HetDex, BOSS, WFMOS, Space) push to 1% distance constraints over a wide range of redshift (0.5<z<3) With 1% constraints need to include 2nd order effects in analysis of BAO positions

Further reading Supernovae Astier et al. (2005), astro-ph/0510447 BAO Blake & Glazebrook (2003), astro-ph/0301632 Seo & Eisenstein (2003), ApJ, 598, 720 Hu & Haiman (2003), astro-ph/0306053